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diff --git a/assignment2.tex b/assignment2.tex new file mode 100644 index 0000000..0b82ded --- /dev/null +++ b/assignment2.tex @@ -0,0 +1,46 @@ +\documentclass[a4paper]{article} + +\usepackage{geometry} +\usepackage[english]{babel} + +\usepackage{enumitem} +\setenumerate[1]{label=\alph*)} + +\usepackage{fancyhdr} +\renewcommand{\headrulewidth}{0pt} +\renewcommand{\footrulewidth}{0pt} +\fancyhead{} +\fancyfoot[C]{Copyright {\textcopyright} 2016 Camil Staps} +\pagestyle{fancy} + +\usepackage{sv} + +\title{Software Verification - assignment 2} +\author{Camil Staps} + +\def\run#1{\mathit{run}_{#1}} +\def\stop#1{\mathit{stop}_{#1}} + +\begin{document} + +\maketitle +\thispagestyle{fancy} + +\setcounter{section}{2} +\section{CTL-properties of processes} + +\begin{enumerate} + \item $\invariantly(\lnot(\run1\land\run2))$. + \item $\potentially(\run1\land\run2)$. + \item $\inevitably\eventually(\run1)$. + \item $\potentially\eventually(\run1)$. + \item $(\potentially(\lnot\run1\until\run2)) \land (\potentially(\lnot\run2\until\run1))$. + \item Impossible: `never' cannot be expressed in CTL: does it mean `in no case whatsoever can this happen' or `there is a path for which this never happens'? But in LTL: $(\always\lnot\run2)\then(\always\run1)$. + \item For the same reason as above we cannot express this in CTL. We cannot express this in LTL either, because `may \dots forever' can only be expressed in CTL. + \item $\invariantly\exists\next\stop{i}$ with $i\in\{1,2\}$. + \item $\invariantly((\forall\lnot\stop1)\then\inevitably\run1)$. + \item $\invariantly(\lnot\run1\then\potentially(\lnot\run1\untilW\run2))$. +\end{enumerate} + +\end{document} + |